High‐Temperature Expansion of the Spin‐½ XY Model

1971 ◽  
Vol 12 (1) ◽  
pp. 61-69 ◽  
Author(s):  
M. Howard Lee
Keyword(s):  
High Temperature ◽  
Xy Model ◽  
Temperature Expansion ◽  
High Temperature Expansion

Dynamical Properties of the Three-Dimensional XY Model. II. Singularity Structure of the Frequency Dependent Susceptibility

1972 ◽  
Vol 50 (20) ◽  
pp. 2415-2420 ◽  
Author(s):  
S. R. Mattingly ◽  
D. D. Betts
Keyword(s):  
High Temperature ◽  
High Frequency ◽  
Three Dimensional ◽  
Xy Model ◽  
Temperature Expansion ◽  
Singularity Structure ◽  
Strong Singularity ◽  
High Temperature Expansion ◽  
Dynamical Properties ◽  
Frequency Temperature

Twenty coefficients are presented in the exact high frequency, high temperature expansion of the perpendicular susceptibility of the spin-1/2 XY model on the f.c.c. lattice. Padé approximant analysis reveals a weak high frequency, temperature independent singularity at ω ≈ (14 ± 2)J/h which we identify with a "quasi-atomic" resonance at ω = 12J/h. We also find a strong singularity at a lower frequency which decreases with decreasing temperature, and for which we have not yet found a satisfying explanation.

MONTE CARLO STUDY OF THE SPIN-1/2 HEISENBERG MODEL IN 1, 2, AND 3 DIMENSIONS

1991 ◽  
Vol 05 (13) ◽  
pp. 907-914 ◽  
Author(s):  
RICHARD J. CRESWICK ◽  
CYNTHIA J. SISSON
Keyword(s):  
Monte Carlo ◽  
High Temperature ◽  
Spin Wave ◽  
Heisenberg Model ◽  
Transition Probability ◽  
Lattice Models ◽  
Wave Theory ◽  
Temperature Expansion ◽  
High Temperature Expansion ◽  
Good Agreement

The properties of the spin-1/2 Heisenberg model on 1, 2, and 3-dimensional lattices are calculated using the Decoupled Cell Method of Homma et al., and these results are compared with high temperature and spin-wave expansions, and with other numerical approaches. The DCM has advantages over other Monte Carlo methods currently in wide use in that the transition probability is positive definite, there is no need to introduce an additional imaginary time, or Trotter, dimension, and the acceptance rate for transitions is comparable to that of classical lattice models. We find very good agreement between the DCM and the high temperature expansion in the temperature region where the high temperature expansion is valid, and reasonably good agreement at low temperatures with spin wave theory. The DCM fails for temperatures T < Tc which decreases with the size of the cell.

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